Ruffini-Horner Algorithm for Complex Arguments

Suppose we need to calculate a value of the polynomial with real coefficients for the complex argument . We divide the polynomial by , where and . The remainder is then a linear function and the value of the polynomial is the value of the remainder. In the table, that is the value at the bottom right.
The table is defined as follows, where the last row is the sum of the higher rows:


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


According to [1, p. 1034] this is called the Collatz contribution.
[1] D. Kurepa, Higher Algebra, Book 2 (in Croatian), Zagreb: Skolska knjiga, 1965.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.